Evaluate the following product without multiplying directly: $76 \times 82$

Factorise $x^{2}+4 y^{2}+25 z^{2}+4 x y-20 y z-10 z x$.

Factorise $x^{3}+2x^{2}-13x+10$.

Factorise the following quadratic polynomial by splitting the middle term:
$6 x^{2}+7 x-20$

The polynomial $p(x) = x^{4} - 2x^{3} + 3x^{2} - ax + 3a - 7$ when divided by $x + 1$ leaves the remainder $19$. Find the value of $a$. Also,find the remainder when $p(x)$ is divided by $x + 2$.

Classify the following as a constant,linear,quadratic,or cubic polynomial:
$3x^3$